Base field \(\Q(\sqrt{3}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 3\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[54, 18, 3w - 9]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 1]$ | $-1$ |
3 | $[3, 3, w]$ | $\phantom{-}0$ |
11 | $[11, 11, -2w + 1]$ | $-3$ |
11 | $[11, 11, 2w + 1]$ | $\phantom{-}6$ |
13 | $[13, 13, w + 4]$ | $-4$ |
13 | $[13, 13, -w + 4]$ | $\phantom{-}5$ |
23 | $[23, 23, -3w + 2]$ | $\phantom{-}3$ |
23 | $[23, 23, 3w + 2]$ | $\phantom{-}3$ |
25 | $[25, 5, 5]$ | $-1$ |
37 | $[37, 37, 2w - 7]$ | $\phantom{-}2$ |
37 | $[37, 37, -2w - 7]$ | $-7$ |
47 | $[47, 47, -4w - 1]$ | $-3$ |
47 | $[47, 47, 4w - 1]$ | $-12$ |
49 | $[49, 7, -7]$ | $-4$ |
59 | $[59, 59, 5w - 4]$ | $\phantom{-}3$ |
59 | $[59, 59, -5w - 4]$ | $\phantom{-}12$ |
61 | $[61, 61, -w - 8]$ | $-10$ |
61 | $[61, 61, w - 8]$ | $-1$ |
71 | $[71, 71, 5w - 2]$ | $-9$ |
71 | $[71, 71, -5w - 2]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w + 1]$ | $1$ |
$3$ | $[3, 3, w]$ | $1$ |